Group #11719247 — subgroups

Subgroups — #11719247

Order 832.

212 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#88190	C₂	1	2	yes	maximal
3	#88180	C₂	1	2	yes	maximal, complemented
4	#88178	C₂	1	2	yes	maximal, complemented
5	#88141	C₂	1	2	yes	maximal, complemented
6	#88133	C₂	1	4	yes	maximal, complemented
7	#88123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₁₃	C₂²	1	2	yes	—
11	C₂×Dic₂₆	C₂²	1	1	yes	characteristic
12	C₂×Dic₂₆	C₂²	1	2	yes	—
13	C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²⋊Dic₁₃	C₂²	1	4	yes	—
17	C₂²⋊Dic₁₃	C₂²	1	4	yes	—
18	C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
19	C₄⋊Dic₁₃	C₂²	1	2	yes	—
20	C₄⋊Dic₁₃	C₂²	1	2	yes	—
21	#6101	C₂²	1	2	yes	—
22	#6101	C₂²	1	4	yes	—
23	C₄×Dic₁₃	C₂²	1	2	yes	—
24	C₄×Dic₁₃	C₂²	1	4	yes	—
25	C₂³×C₁₃	C₂³	1	2	yes	—
26	D₄×C₁₃	—	2	2	no	—
27	C₂×C₄×C₁₃	—	2	4	no	—
28	C₂×C₄×C₁₃	C₂³	1	2	yes	—
29	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×Dic₁₃	C₂³	1	2	yes	—
33	C₂×Dic₁₃	C₂³	1	2	yes	—
34	C₂×Dic₁₃	C₂³	1	4	yes	—
35	Dic₂₆	—	2	4	no	—
36	Dic₂₆	—	2	2	no	—
37	#556	—	13	1	no	maximal, Sylow
38	C₂²×C₁₃	—	2	2	no	—
39	C₂²×C₁₃	—	2	2	no	—
40	C₂²×C₁₃	—	2	2	no	—
41	C₂²×C₁₃	C₂⁴	1	1	yes	characteristic
42	C₄×C₁₃	—	2	2	no	—
43	C₄×C₁₃	—	2	1	no	—
44	C₄×C₁₃	#41	1	2	yes	—
45	C₄×C₁₃	#41	1	2	yes	—
46	Dic₁₃	—	2	4	no	—
47	Dic₁₃	—	2	2	no	—
48	Dic₁₃	—	2	2	no	—
49	C₄⋊Q₈	—	13	1	no	—
50	#126	—	13	4	no	—
51	#124	—	13	2	no	—
52	C₂²⋊Q₈	—	13	2	no	—
53	C₄×Q₈	—	13	2	no	—
54	C₄×Q₈	—	13	1	no	—
55	C₄×D₄	D₁₃	1	1	yes	characteristic
56	#117	—	13	2	no	—
57	C₂×C₁₃	—	4	2	no	—
58	C₂×C₁₃	C₂×#41	1	1	yes	characteristic
59	C₂×C₁₃	C₂×#41	1	1	yes	characteristic
60	C₂×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
61	C₂×Q₈	—	13	1	no	—
62	C₂×Q₈	—	13	2	no	—
63	C₂×D₄	C₂×D₁₃	1	1	yes	characteristic
64	C₂²×C₄	C₂×D₁₃	1	2	yes	—
65	C₄⋊C₄	—	13	1	no	—
66	C₄⋊C₄	—	13	2	no	—
67	C₄⋊C₄	—	13	4	no	—
68	C₄⋊C₄	—	13	2	no	—
69	C₄⋊C₄	—	13	2	no	—
70	C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
71	C₂²⋊C₄	—	13	4	no	—
72	C₂²⋊C₄	—	13	4	no	—
73	C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
74	C₄²	—	13	4	no	—
75	C₄²	—	13	2	no	—
76	C₄²	C₂×D₁₃	1	1	yes	characteristic
77	C₁₃	#556	1	1	yes	characteristic, complemented, Sylow
78	C₂³	C₂²×D₁₃	1	2	yes	—
79	Q₈	—	26	4	no	—
80	Q₈	—	26	2	no	—
81	D₄	—	2	2	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	13	2	no	—
84	C₂×C₄	—	13	4	no	—
85	C₂×C₄	—	13	2	no	—
86	C₂×C₄	C₂²×D₁₃	1	2	yes	—
87	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
88	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
89	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	—	2	2	no	—
92	C₂²	—	2	2	no	—
93	C₂²	C₂³×D₁₃	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	2	1	no	—
96	C₄	—	26	4	no	—
97	C₄	—	26	2	no	—
98	C₄	—	26	2	no	—
99	C₄	#6127	1	2	yes	—
100	C₄	#6129	1	2	yes	—
101	C₂	—	4	2	no	—
102	C₂	C₂×#6127	1	1	yes	characteristic
103	C₂	C₂×#6129	1	1	yes	characteristic
104	C₂	#88257	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₄×C₁₃

C₂

yes

maximal, characteristic

#88190

C₂

yes

maximal

#88180

C₂

yes

maximal, complemented

#88178

C₂

yes

maximal, complemented

#88141

C₂

yes

maximal, complemented

#88133

C₂

yes

maximal, complemented

#88123

C₂

yes

maximal, characteristic, complemented

C₄×Dic₂₆

C₂

yes

maximal, characteristic, complemented

C₂×D₄×C₁₃

C₂²

yes

characteristic

C₂²×C₄×C₁₃

C₂²

yes

—

C₂×Dic₂₆

C₂²

yes

characteristic

C₂×Dic₂₆

C₂²

yes

—

C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₁₃×C₂²⋊C₄

C₂²

yes

—

C₄²×C₁₃

C₂²

yes

characteristic

C₂²⋊Dic₁₃

C₂²

yes

—

C₂²⋊Dic₁₃

C₂²

yes

—

C₄⋊Dic₁₃

C₂²

yes

characteristic

C₄⋊Dic₁₃

C₂²

yes

—

C₄⋊Dic₁₃

C₂²

yes

—

#6101

C₂²

yes

—

#6101

C₂²

yes

—

C₄×Dic₁₃

C₂²

yes

—

C₄×Dic₁₃

C₂²

yes

—

C₂³×C₁₃

C₂³

yes

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂³

yes

—

C₂×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₄×C₁₃

C₂³

yes

characteristic

C₂×Dic₁₃

C₂³

yes

—

C₂×Dic₁₃

C₂³

yes

—

C₂×Dic₁₃

C₂³

yes

—

Dic₂₆

—

Dic₂₆

—

#556

—

maximal, Sylow

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂⁴

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#41

yes

—

C₄×C₁₃

#41

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₄⋊Q₈

—

#126

—

#124

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×D₄

D₁₃

yes

characteristic

#117

—

C₂×C₁₃

—

C₂×C₁₃

C₂×#41

yes

characteristic

C₂×C₁₃

C₂×#41

yes

characteristic

C₂×C₁₃

2₋¹⁺⁴

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

C₂×D₁₃

yes

characteristic

C₂²×C₄

C₂×D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₁₃

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×D₁₃

yes

characteristic

C₁₃

#556

yes

characteristic, complemented, Sylow

C₂³

C₂²×D₁₃

yes

—

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₁₃

yes

—

C₂×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₄

C₂²×D₁₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂³×D₁₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#6127

yes

—

100

C₄

#6129

yes

—

101

C₂

—

102

C₂

C₂×#6127

yes

characteristic

103

C₂

C₂×#6129

yes

characteristic

104

C₂

#88257

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁴
Fitting	C₄×D₄×C₁₃	C₂
prime radical	C₂×D₄×C₁₃	C₂²
hypercenter	C₄×D₄	D₁₃
hypocenter	C₁₃	#556
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₃

commutator, socle, cosocle

C₂²×C₁₃

C₂⁴

Fitting

C₄×D₄×C₁₃

C₂

prime radical

C₂×D₄×C₁₃

C₂²

hypercenter

C₄×D₄

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂² ◁ C₄×D₄

N	H ≅ G/N	type
3. #88180	C₂	semidirect
4. #88178	C₂	semidirect
5. #88141	C₂	semidirect
6. #88133	C₂	semidirect
7. #88123	C₂	semidirect
8. C₄×Dic₂₆	C₂	semidirect
77. C₁₃	#556	semidirect

H ≅ G/N

type

3. #88180

C₂

semidirect

4. #88178

C₂

semidirect

5. #88141

C₂

semidirect

6. #88133

C₂

semidirect

7. #88123

C₂

semidirect

8. C₄×Dic₂₆

C₂

semidirect

77. C₁₃

#556

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×D₄×C₁₃	2
#88190	2
#88180	2
#88178	2
#88141	2
#88133	2
#88123	2
C₄×Dic₂₆	2
#556	13

subgroup

index

C₄×D₄×C₁₃

C₄×Dic₂₆

Subgroups — #11719247

Conjugacy classes of subgroups

Complements

Maximal subgroups